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Flow pattern analysis of linear gradient flow distribution

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Abstract

This paper uses the Oseen transformation to solve the differential equations governing motion of the vertical linear gradient flow distribution close to a wall surface. The Navier-Stokes equations are used to consider the inertia term along the flow direction. A novel contour integral method is used to solve the complex Airy function. The boundary conditions of linear gradient flow distribution for finite problems are determined. The vorticity function, the pressure function, and the turbulent velocity profiles are provided, and the stability of particle trajectories is studied. An L x -function form of the third derivative circulation is used to to simplify the solution. Theoretical results are compared with the experimental measurements with satisfactory agreement.

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Authors and Affiliations

  1. School of Civil Engineering & Key Laboratory of Harbor & Ocean Engineering Ministry of Education, Tianjin University, Tianjin, 300072, P. R. China

    Da-ming Li & Xiao-yu Li

  2. Civil and Environmental Engineering, Johns Hopkins University, Baltimore, 21218, USA

    Xiao-yu Li & R. J. Farahani

  3. Civil Engineering, The University of Adelaide, Adelaide, 5005, Australia

    Yan-qing Li

Authors
  1. Da-ming Li
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  2. Xiao-yu Li
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  3. Yan-qing Li
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  4. R. J. Farahani
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Corresponding author

Correspondence to Xiao-yu Li.

Additional information

Project supported by the National Natural Science foundation of China (No. 51079095) and the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (No. 51021004)

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Li, Dm., Li, Xy., Li, Yq. et al. Flow pattern analysis of linear gradient flow distribution. Appl. Math. Mech.-Engl. Ed. 36, 81–106 (2015). https://doi.org/10.1007/s10483-015-1920-9

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  • DOI: https://doi.org/10.1007/s10483-015-1920-9

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Chinese Library Classification

2010 Mathematics Subject Classification

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